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Using the exact results of the O(3) nonlinear sigma model (NLSM) and a fewquantitative numerical data for integer-spin antiferromagnetic (AF) chains, wesystematically estimate all magnon excitation energies of N-leg integer-spin AFladders and tubes in the weak-interchain-coupling regime. Our method is basedon a first-order perturbation theory for the strength of the interchaincoupling. It can deal with any kind of interchain interactions, in principle.We confirm that results of the perturbation theory are in good agreement withthose of a quantum Monte Carlo simulation and with our recent study based on asaddle-point approximation of the NLSM [Phys. Rev. B 72, 104438 (2005)]. Ourtheory further supports the existence of a Haldane (gapped) phase even in ad-dimensional (d\geq 2) spatially anisotropic integer-spin AF model, if theexchange coupling in one direction is sufficiently strong compared with thosein all the other directions. The strategy in this paper is applicable to otherN-leg systems consisting of gapped chains which low-energy physics is exactlyor quantitatively known.Comment: 11 pages, 4 figures, Revtex, published version, see also  cond-mat/0506049 (PRB72, 104438 (2005)

physical review. b, condensed matter and materials physics

Magnon bands of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-leg integer-spin antiferromagnetic systems in the weak-interchain-coupling regime

Magnon bands ofN-leg integer-spin antiferromagnetic systems in the weak-interchain-coupling regime